For example, if you photographed a Ciel and Sebastian (Black Butler) before, would you photograph these characters again if a different cosplayer asked you to? Would you only do this if it's a special circumstance (close friend, etc)?

When I did this, I realized I didn't have as many ideas the second time around, and I wasn't as excited about taking the photos.

In order to agree to a shoot, I generally have to be inspired by it. And I can be inspired several times by a given character, if the cosplayers have their own ideas for the theme and location of the shoot, and I think the shoot will be interesting.
But I'm very picky when it comes to extended shoots anyway, either I'm a big fan of the series, or there's a specific idea behind the shoot (that the cosplayer has come up with, or that I have), I'm not really the kind to completely improvise photoshoots, or to do them one after another during cons. I generally take my time, at least two hours, and it's generally no more than one in a day.